Right isosceles triangle

The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into two equal segments. The length of one segment is 5 cm. What is the area of the triangle?

Correct answer:

S =  25 cm²

Step-by-step explanation:

$$\begin{gathered} c_1=5\text{cm} \\ {c}_2=c_1=5\text{cm} \\ c=c_1+c_2=5+5=10\text{cm} \\ h=\sqrt{c_1\cdot c_2}=\sqrt{5\cdot 5}=5\text{cm} \\ S=\frac{c\cdot h}{2}=\frac{10\cdot 5}{2}=25{\text{cm}}^2 \end{gathered}$$

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